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Question

The speed v of a particle moving along a straight line, when it is at a distance x from a fixed point on the line, is given by v2=1449x2.
Choose the wrong option.

A
Displacement of the particle distance moved by it
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B
The magnitude of acceleration at a distance 3 units from the fixed point is 27 units
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C
The motion is simple harmonic with T=π3 units
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D
The maximum displacement from the fixed point is 4 units
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Solution

The correct option is C The motion is simple harmonic with T=π3 units
Given,
v2=1449x2
Comparing this with
v=ωA2x2
v2=ω2A2ω2x2
we get,
ω2=9ω=±3
and
ω2A2=144A=4 units
So, option (d) is true.
We know that, |a|=ω2x|a|=(9)(3)=27 units
ω=2πT we get , T=2π3 units
So, option (b) is true and option (c) is wrong.
Since, statement (a) is always correct.
we can say that, option (c) is wrong answer.

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